A Legacy of EM Algorithms

被引:3
|
作者
Lange, Kenneth [1 ,2 ,3 ]
Zhou, Hua [1 ,4 ]
机构
[1] Univ Calif Los Angeles, Dept Computat Med, Los Angeles, CA 90095 USA
[2] Univ Calif Los Angeles, Dept Human Genet, Los Angeles, CA 90095 USA
[3] Univ Calif Los Angeles, Dept Stat, Los Angeles, CA 90095 USA
[4] Univ Calif Los Angeles, Dept Biostat, Los Angeles, CA 90095 USA
关键词
EM algorithm; MM algorithm; variance component model; longitudinal data analysis; MAJORIZATION; OPTIMIZATION; LIKELIHOOD;
D O I
10.1111/insr.12526
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Nan Laird has an enormous and growing impact on computational statistics. Her paper with Dempster and Rubin on the expectation-maximisation (EM) algorithm is the second most cited paper in statistics. Her papers and book on longitudinal modelling are nearly as impressive. In this brief survey, we revisit the derivation of some of her most useful algorithms from the perspective of the minorisation-maximisation (MM) principle. The MM principle generalises the EM principle and frees it from the shackles of missing data and conditional expectations. Instead, the focus shifts to the construction of surrogate functions via standard mathematical inequalities. The MM principle can deliver a classical EM algorithm with less fuss or an entirely new algorithm with a faster rate of convergence. In any case, the MM principle enriches our understanding of the EM principle and suggests new algorithms of considerable potential in high-dimensional settings where standard algorithms such as Newton's method and Fisher scoring falter.
引用
收藏
页码:S52 / S66
页数:15
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